In the opening paragraph, Bacon establishes the importance of friendship by implication when he says "whatsoever is delighted in solitude is either a wild beast or a god." He expands on this theme in the same paragraph by saying that, without friends, the "world is but a wilderness."
Bacon's essay is centered on what he calls the "fruit of friendship," of which there are three, and the first is the ability to get rid of all one's frustrations by having a true friend to listen. Bacon lived in an era when men believed that our bodies were controlled by "humours"--earth, air, fire and water--and if the humours became unbalanced in our bodies, we got sick. Bacon likens the balance of humours in the body to balance in the mind, and one restores balance to the mind by unburdening onself to a friend.
The next section of the essay is a long discussion of friendships and failed friendships in classical Roman history, and then Bacon articulates the "second fruit of friendship," which is the result of discussing one's problems with a sympathetic friends, and in the process of "communicating and discoursing with another," one actually becomes "wiser than himself." But, the second fruit has another half that is just as important, and that is counsel from the friend, which, according to Bacon, is "drier and purer" than the counsel that comes from within oneself.
Bacon compares the third fruit of friendship to a pomegranate, which hundreds of kernels. Bacon argues that there are many things a man cannot do for himself--praise himself (modestly), ask for help--that a friend can do for him with no embarrassment. These are among the many kernels of friendship embodied in the third fruit.